# Part B: FH Long-Difference Robustness

Tests whether the S×Z interaction survives in long-difference specifications to address persistence/nonstationarity concerns.

## Model Comparison

| Model | N | Countries | R² | ρ |
|-------|---|-----------|----|----|
| M5a-Annual: FH baseline | 5,661 | 169 | 0.071 | 0.850 |
| M5c-Annual: FH + S×Z | 5,661 | 169 | 0.180 | 0.841 |
| M5a-5yr avg: FH baseline | 1,188 | 169 | 0.173 | 0.653 |
| M5c-5yr avg: FH + S×Z | 1,188 | 169 | 0.236 | 0.656 |
| M5a-10yr avg: FH baseline | 698 | 169 | 0.175 | 0.578 |
| M5c-10yr avg: FH + S×Z | 698 | 169 | 0.253 | 0.574 |

## Key Coefficients

| Variable | Model | Coef | SE | p-value |
|----------|-------|------|----|---------|
| savings_gdp | M5a-Annual: FH baseline | 0.0541*** | 0.0068 | 0.0000 |
| savings_gdp | M5c-Annual: FH + S×Z | 0.2594*** | 0.0260 | 0.0000 |
| savings_gdp | M5a-5yr avg: FH baseline | 0.1645*** | 0.0143 | 0.0000 |
| savings_gdp | M5c-5yr avg: FH + S×Z | 0.3430*** | 0.0446 | 0.0000 |
| savings_gdp | M5a-10yr avg: FH baseline | 0.1718*** | 0.0172 | 0.0000 |
| savings_gdp | M5c-10yr avg: FH + S×Z | 0.3451*** | 0.0519 | 0.0000 |
| savings_x_Z1 | M5c-Annual: FH + S×Z | 2.3185*** | 0.2848 | 0.0000 |
| savings_x_Z1 | M5c-5yr avg: FH + S×Z | 3.3036*** | 0.4888 | 0.0000 |
| savings_x_Z1 | M5c-10yr avg: FH + S×Z | 3.4992*** | 0.6025 | 0.0000 |
| savings_x_Z2 | M5c-Annual: FH + S×Z | -0.3970*** | 0.0422 | 0.0000 |
| savings_x_Z2 | M5c-5yr avg: FH + S×Z | -0.5193*** | 0.0752 | 0.0000 |
| savings_x_Z2 | M5c-10yr avg: FH + S×Z | -0.5254*** | 0.0933 | 0.0000 |
| savings_x_Z3 | M5c-Annual: FH + S×Z | 0.0178*** | 0.0017 | 0.0000 |
| savings_x_Z3 | M5c-5yr avg: FH + S×Z | 0.0220*** | 0.0031 | 0.0000 |
| savings_x_Z3 | M5c-10yr avg: FH + S×Z | 0.0215*** | 0.0039 | 0.0000 |